For any positive integer n, define fn:(0,∞)→ R as
fn(x)=∑ for j=1,n tan-1(1/(1+(x+j)(x+j-1))) for all x ∈(0,∞)
(Here, the inverse trigonometric function tan -1x assumes values in (-π/2,π/2))
Then, which of the following statement(s) is (are) TRUE ?
(A) ∑ for j=1,5 tan2(fi(0))=55
(B)∑ for j=1,10 (1+fj'(0))sec2(fj(0))=10
(C) For any fixed positive integer n, lim x→∞ tan (fn(x))=1/n
(D) For any fixed positive integer n, lim x→∞ sec2 (fn (x))=1
